Question

Plzz help me with this trig proof ​

Answer 1

Explanation:

`(sin3A)/(cosA) + (cos3A)/(sinA)`

`(sin3AsinA)/(sinAcosA) + (cos3AcosA)/(sinAcosA)`

`(cos3AcosA + sin3AsinA)/(sinAcosA)`

From here, remember the following identity:

`cos(X - Y) = cosXcosY + sinXsinY`

If we set
`X = 3A` and
`Y = A`, we get the following:

`cos(3A - A) = cos2A = cos3AcosA + sin3AsinA`

we can then plug this back into our original equation:

`(cos2A)/(sinAcosA)`

From here, remember the following identity:

`cos2A = cos^(2)A - sin^(2)A`

we can then plug this back into our original equation:

`(cos^(2)A - sin^(2)A)/(sinAcosA)`

`(cos^(2)A)/(sinAcosA) - (sin^(2)A)/(sinAcosA)`

`(cosA)/(sinA) - (sinA)/(cosA)`

`cotA - tanA`